#include <cmath>
#include <complex>

Include dependency graph for GSLComplex.h:

This graph shows which files directly or indirectly include this file:

Classes
struct	gsl_complex
	Complex number stored as \((\Re, \Im)\). More...

Macros
#define	GSL_REAL(z) ((z).dat[0])
	Access real part of a `gsl_complex`.

#define	GSL_IMAG(z) ((z).dat[1])
	Access imaginary part of a `gsl_complex`.

Functions
gsl_complex	gsl_complex_rect (double x, double y)
	Construct \(z = x + i y\).

gsl_complex	gsl_complex_polar (double r, double theta)
	Construct \(z = r e^{i\theta}\).

double	gsl_complex_arg (gsl_complex z)
	Argument (phase) \(\arg(z)\).

double	gsl_complex_abs (gsl_complex z)
	Magnitude \(\|z\|\).

double	gsl_complex_abs2 (gsl_complex z)
	Squared magnitude \(\|z\|^2\).

gsl_complex	gsl_complex_add (gsl_complex a, gsl_complex b)
	Sum \(a + b\).

gsl_complex	gsl_complex_sub (gsl_complex a, gsl_complex b)
	Difference \(a - b\).

gsl_complex	gsl_complex_mul (gsl_complex a, gsl_complex b)
	Product \(a \cdot b\).

gsl_complex	gsl_complex_div (gsl_complex a, gsl_complex b)
	Quotient \(a / b\).

gsl_complex	gsl_complex_add_real (gsl_complex a, double x)
	Add real scalar \(a + x\).

gsl_complex	gsl_complex_sub_real (gsl_complex a, double x)
	Subtract real scalar \(a - x\).

gsl_complex	gsl_complex_mul_real (gsl_complex a, double x)
	Multiply by real scalar \(a \cdot x\).

gsl_complex	gsl_complex_div_real (gsl_complex a, double x)
	Divide by real scalar \(a / x\).

gsl_complex	gsl_complex_conjugate (gsl_complex a)
	Complex conjugate \(\overline{a}\).

gsl_complex	gsl_complex_inverse (gsl_complex a)
	Multiplicative inverse \(1/a\).

gsl_complex	gsl_complex_negative (gsl_complex a)
	Negation \(-a\).

gsl_complex	gsl_complex_sqrt (gsl_complex a)
	Complex square root \(\sqrt{a}\).

gsl_complex	gsl_complex_exp (gsl_complex a)
	Complex exponential \(e^{a}\).

gsl_complex	gsl_complex_log (gsl_complex a)
	Complex natural logarithm \(\log(a)\).

gsl_complex	gsl_complex_sin (gsl_complex a)
	Complex sine \(\sin(a)\).

gsl_complex	gsl_complex_cos (gsl_complex a)
	Complex cosine \(\cos(a)\).

gsl_complex	gsl_complex_pow (gsl_complex a, gsl_complex b)
	Complex power \(a^b\).

gsl_complex	gsl_complex_tanh (gsl_complex a)
	Complex hyperbolic tangent \(\tanh(a)\).

Macro Definition Documentation

◆ GSL_IMAG

#define GSL_IMAG ( z ) ((z).dat[1])

Access imaginary part of a gsl_complex.

Definition at line 43 of file GSLComplex.h.

◆ GSL_REAL

#define GSL_REAL ( z ) ((z).dat[0])

Access real part of a gsl_complex.

Definition at line 41 of file GSLComplex.h.

Function Documentation

◆ gsl_complex_abs()

double gsl_complex_abs ( gsl_complex z )

inline

Magnitude \(|z|\).

Parameters

z	Input: complex value.

Returns: Output: \(|z|\).

Definition at line 67 of file GSLComplex.h.

Referenced by gsl_linalg_complex_LU_decomp(), and TEST_F().

◆ gsl_complex_abs2()

double gsl_complex_abs2 ( gsl_complex z )

inline

Squared magnitude \(|z|^2\).

Parameters

z	Input: complex value.

Returns: Output: \(|z|^2\).

Definition at line 72 of file GSLComplex.h.

References gsl_complex::dat.

◆ gsl_complex_add()

gsl_complex gsl_complex_add	(	gsl_complex	a,
		gsl_complex	b
	)

inline

Sum \(a + b\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: first operand.
b	Input: second operand.

Returns: Output: \(a + b\).

Definition at line 79 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by gsl_blas_zgemm(), gsl_blas_zgemv(), gsl_linalg_complex_LU_invert(), gsl_matrix_complex_add(), gsl_vector_complex_add(), interpolation::operator+(), interpolation::operator+=(), and TEST_F().

◆ gsl_complex_add_real()

gsl_complex gsl_complex_add_real	(	gsl_complex	a,
		double	x
	)

inline

Add real scalar \(a + x\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.
x	Input: real scalar.

Returns: Output: \(a + x\).

Definition at line 116 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by interpolation::operator+(), interpolation::operator+(), and interpolation::operator+=().

◆ gsl_complex_arg()

double gsl_complex_arg ( gsl_complex z )

inline

Argument (phase) \(\arg(z)\).

Parameters

z	Input: complex value.

Returns: Output: phase angle.

Definition at line 62 of file GSLComplex.h.

Referenced by TEST_F().

◆ gsl_complex_conjugate()

gsl_complex gsl_complex_conjugate ( gsl_complex a )

inline

Complex conjugate \(\overline{a}\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\overline{a}\).

Definition at line 151 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by gsl_blas_zgemm(), gsl_blas_zgemv(), and TEST_F().

◆ gsl_complex_cos()

gsl_complex gsl_complex_cos ( gsl_complex a )

inline

Complex cosine \(\cos(a)\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\cos(a)\).

Definition at line 208 of file GSLComplex.h.

◆ gsl_complex_div()

gsl_complex gsl_complex_div	(	gsl_complex	a,
		gsl_complex	b
	)

inline

Quotient \(a / b\).

Parameters

a	Input: numerator.
b	Input: denominator.

Returns: Output: \(a / b\).

Definition at line 106 of file GSLComplex.h.

Referenced by gsl_linalg_complex_LU_decomp(), gsl_linalg_complex_LU_invert(), interpolation::operator/(), interpolation::operator/(), interpolation::operator/=(), and TEST_F().

◆ gsl_complex_div_real()

gsl_complex gsl_complex_div_real	(	gsl_complex	a,
		double	x
	)

inline

Divide by real scalar \(a / x\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.
x	Input: real scalar.

Returns: Output: \(a / x\).

Definition at line 143 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by interpolation::operator/(), and interpolation::operator/=().

◆ gsl_complex_exp()

gsl_complex gsl_complex_exp ( gsl_complex a )

inline

Complex exponential \(e^{a}\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(e^{a}\).

Definition at line 181 of file GSLComplex.h.

Referenced by TEST_F().

◆ gsl_complex_inverse()

gsl_complex gsl_complex_inverse ( gsl_complex a )

inline

Multiplicative inverse \(1/a\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(1/a\).

Definition at line 157 of file GSLComplex.h.

◆ gsl_complex_log()

gsl_complex gsl_complex_log ( gsl_complex a )

inline

Complex natural logarithm \(\log(a)\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\log(a)\).

Definition at line 190 of file GSLComplex.h.

Referenced by TEST_F().

◆ gsl_complex_mul()

gsl_complex gsl_complex_mul	(	gsl_complex	a,
		gsl_complex	b
	)

inline

Product \(a \cdot b\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: first operand.
b	Input: second operand.

Returns: Output: \(a b\).

Definition at line 97 of file GSLComplex.h.

Referenced by gsl_blas_zgemm(), gsl_blas_zgemv(), gsl_linalg_complex_LU_decomp(), gsl_linalg_complex_LU_det(), gsl_linalg_complex_LU_invert(), gsl_matrix_complex_scale(), gsl_vector_complex_scale(), interpolation::operator*(), interpolation::operator*=(), and TEST_F().

◆ gsl_complex_mul_real()

gsl_complex gsl_complex_mul_real	(	gsl_complex	a,
		double	x
	)

inline

Multiply by real scalar \(a \cdot x\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.
x	Input: real scalar.

Returns: Output: \(a x\).

Definition at line 134 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by interpolation::operator*(), interpolation::operator*(), and interpolation::operator*=().

◆ gsl_complex_negative()

gsl_complex gsl_complex_negative ( gsl_complex a )

inline

Negation \(-a\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(-a\).

Definition at line 166 of file GSLComplex.h.

References gsl_complex::dat.

◆ gsl_complex_polar()

gsl_complex gsl_complex_polar	(	double	r,
		double	theta
	)

inline

Construct \(z = r e^{i\theta}\).

Parameters

r	Input: magnitude.
theta	Input: phase angle.

Returns: Output: complex value \(r e^{i\theta}\).

Definition at line 55 of file GSLComplex.h.

Referenced by TEST_F().

◆ gsl_complex_pow()

gsl_complex gsl_complex_pow	(	gsl_complex	a,
		gsl_complex	b
	)

inline

Complex power \(a^b\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: base.
b	Input: exponent.

Returns: Output: \(a^b\).

Definition at line 218 of file GSLComplex.h.

◆ gsl_complex_rect()

gsl_complex gsl_complex_rect	(	double	x,
		double	y
	)

inline

Construct \(z = x + i y\).

Parameters

x	Input: real part.
y	Input: imaginary part.

Returns: Output: complex value \(x + i y\).

Definition at line 49 of file GSLComplex.h.

Referenced by TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), TEST_F(), and TEST_F().

◆ gsl_complex_sin()

gsl_complex gsl_complex_sin ( gsl_complex a )

inline

Complex sine \(\sin(a)\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\sin(a)\).

Definition at line 199 of file GSLComplex.h.

◆ gsl_complex_sqrt()

gsl_complex gsl_complex_sqrt ( gsl_complex a )

inline

Complex square root \(\sqrt{a}\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\sqrt{a}\).

Definition at line 172 of file GSLComplex.h.

◆ gsl_complex_sub()

gsl_complex gsl_complex_sub	(	gsl_complex	a,
		gsl_complex	b
	)

inline

Difference \(a - b\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: first operand.
b	Input: second operand.

Returns: Output: \(a - b\).

Definition at line 88 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by gsl_eigen_nonsymmv(), gsl_linalg_complex_LU_decomp(), gsl_linalg_complex_LU_invert(), interpolation::operator-(), interpolation::operator-=(), and TEST_F().

◆ gsl_complex_sub_real()

gsl_complex gsl_complex_sub_real	(	gsl_complex	a,
		double	x
	)

inline

Subtract real scalar \(a - x\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.
x	Input: real scalar.

Returns: Output: \(a - x\).

Definition at line 125 of file GSLComplex.h.

References gsl_complex::dat.

Referenced by interpolation::operator-(), interpolation::operator-(), and interpolation::operator-=().

◆ gsl_complex_tanh()

gsl_complex gsl_complex_tanh ( gsl_complex a )

inline

Complex hyperbolic tangent \(\tanh(a)\).

See also: https://www.gnu.org/software/gsl/doc/html/complex.html

Parameters

a	Input: complex operand.

Returns: Output: \(\tanh(a)\).

Definition at line 227 of file GSLComplex.h.

Referenced by TEST_F().

Classes

Macros

Functions

Macro Definition Documentation

◆ GSL_IMAG

◆ GSL_REAL

Function Documentation

◆ gsl_complex_abs()

◆ gsl_complex_abs2()

◆ gsl_complex_add()

◆ gsl_complex_add_real()

◆ gsl_complex_arg()

◆ gsl_complex_conjugate()

◆ gsl_complex_cos()

◆ gsl_complex_div()

◆ gsl_complex_div_real()

◆ gsl_complex_exp()

◆ gsl_complex_inverse()

◆ gsl_complex_log()

◆ gsl_complex_mul()

◆ gsl_complex_mul_real()

◆ gsl_complex_negative()

◆ gsl_complex_polar()

◆ gsl_complex_pow()

◆ gsl_complex_rect()

◆ gsl_complex_sin()

◆ gsl_complex_sqrt()

◆ gsl_complex_sub()

◆ gsl_complex_sub_real()

◆ gsl_complex_tanh()